Plug the phone in to wall charger, turn vibrate on and off. Try a different charger and cable. Clean the dock port of all lint/dust. Check for obvious bent pins etc If still no response the problem may be the dock connector.
At this stage replacing the dock is the cheapest option. Try the above tips and then get back to us. It'd be a shame to declare motherboard damage without trying the simple fixes first.
ok.. there are a few choices..you need to look under the metal shield to inspect the parts for damage this is a guide to remove the shield How to remove the motherboard shield? . take a look at this picture and compare to what you see on your ..motherboard choice no 1 is the fuse from battery.. choice no 2 is the power management ic. you will need some skills with a soldering iron for no1 and no 2 is probably something you won't have the tools for , you may need to take it to a shop/friend/or cut your losses and sell on.